For the devices in the high carrier density limit (2B at \(V_\text{GIL} =\)  3.7 V, 3A, 3B), \(I_C R_N\)  exceeds \(\pi \Delta /e\)  by a factor of 1.2 - 2. A natural explanation is a crossover from an SNS junction to an SS'S constriction or wire. Establishing a crisp picture requires further study, but two frameworks can be invoked as useful starting points. One one hand, \(I_C R_N\)  in a superconducting wire (S') connecting two superconducting reservoirs (S) is expected to increase with length until the onset of decoherence, and can exceed \(\pi \Delta /e\)  [1]}. On the other hand, one can make a comparison to the STO leads themselves, which show ‘‘weak superconductivity’’ with a relatively small critical current. A 20x20 \(\mu \) m square of STO in the leads shows \(eI_C R_N/\Delta = \)  4.5 near devices 1A and 1B and 3.2 near devicees 3A and 3B. In [2]}, a 50 \(\mu \) m long and 20 \(\mu \) m wide LAO/STO Hall bar has been documented to show \(eI_C R_N/\Delta = \)  25-70. This was rationalized in terms of an interconnected Josephson junction array, where \(I_C R_N\)  scales with its size and can easily exceed \(\Delta /e\) . For the case of a square array of \(N_\text{JJ} \times N_\text{JJ}\)  junctions, \(eI_C R_N/\Delta = N_\text{JJ}\pi /2\)  [3]}.
